<!doctype html>
<html>
<head>
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>

<link href='https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text/css' /><style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; --title-bar-height:20px; }
.mac-os-11 { --title-bar-height:28px; }
html { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }
body { margin: 0px; padding: 0px; height: auto; inset: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
iframe { margin: auto; }
a.url { word-break: break-all; }
a:active, a:hover { outline: 0px; }
.in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }
#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }
#write.first-line-indent p { text-indent: 2em; }
#write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }
#write.first-line-indent li { margin-left: 2em; }
.for-image #write { padding-left: 8px; padding-right: 8px; }
body.typora-export { padding-left: 30px; padding-right: 30px; }
.typora-export .footnote-line, .typora-export li, .typora-export p { white-space: pre-wrap; }
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  .CodeMirror-gutters { display: none !important; }
}
#write li > figure:last-child { margin-bottom: 0.5rem; }
#write ol, #write ul { position: relative; }
img { max-width: 100%; vertical-align: middle; image-orientation: from-image; }
button, input, select, textarea { color: inherit; font: inherit; }
input[type="checkbox"], input[type="radio"] { line-height: normal; padding: 0px; }
*, ::after, ::before { box-sizing: border-box; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p, #write pre { width: inherit; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p { position: relative; }
p { line-height: inherit; }
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h2 { font-size: 1.8rem; }
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h4 { font-size: 1.4rem; }
h5 { font-size: 1.2rem; }
h6 { font-size: 1rem; }
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a { cursor: pointer; }
sup.md-footnote { padding: 2px 4px; background-color: rgba(238, 238, 238, 0.7); color: rgb(85, 85, 85); border-radius: 4px; cursor: pointer; }
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#write input[type="checkbox"] { cursor: pointer; width: inherit; height: inherit; }
figure { overflow-x: auto; margin: 1.2em 0px; max-width: calc(100% + 16px); padding: 0px; }
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tr { break-inside: avoid; break-after: auto; }
thead { display: table-header-group; }
table { border-collapse: collapse; border-spacing: 0px; width: 100%; overflow: auto; break-inside: auto; text-align: left; }
table.md-table td { min-width: 32px; }
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.footnotes { opacity: 0.8; font-size: 0.9rem; margin-top: 1em; margin-bottom: 1em; }
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.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }
li div { padding-top: 0px; }
blockquote { margin: 1rem 0px; }
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}
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pre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }
p > .md-image:only-child:not(.md-img-error) img, p > img:only-child { display: block; margin: auto; }
#write.first-line-indent p > .md-image:only-child:not(.md-img-error) img { left: -2em; position: relative; }
p > .md-image:only-child { display: inline-block; width: 100%; }
#write .MathJax_Display { margin: 0.8em 0px 0px; }
.md-math-block { width: 100%; }
.md-math-block:not(:empty)::after { display: none; }
.MathJax_ref { fill: currentcolor; }
[contenteditable="true"]:active, [contenteditable="true"]:focus, [contenteditable="false"]:active, [contenteditable="false"]:focus { outline: 0px; box-shadow: none; }
.md-task-list-item { position: relative; list-style-type: none; }
.task-list-item.md-task-list-item { padding-left: 0px; }
.md-task-list-item > input { position: absolute; top: 0px; left: 0px; margin-left: -1.2em; margin-top: calc(1em - 10px); border: none; }
.math { font-size: 1rem; }
.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }
.md-toc-content { position: relative; margin-left: 0px; }
.md-toc-content::after, .md-toc::after { display: none; }
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.md-toc-h6 .md-toc-inner { margin-left: 10em; }
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}
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.footnote-line a:not(.reversefootnote) { color: inherit; }
.md-attr { display: none; }
.md-fn-count::after { content: "."; }
code, pre, samp, tt { font-family: var(--monospace); }
kbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }
.md-comment { color: rgb(162, 127, 3); opacity: 0.6; font-family: var(--monospace); }
code { text-align: left; vertical-align: initial; }
a.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }
.os-windows.monocolor-emoji .md-emoji { font-family: "Segoe UI Symbol", sans-serif; }
.md-diagram-panel > svg { max-width: 100%; }
[lang="flow"] svg, [lang="mermaid"] svg { max-width: 100%; height: auto; }
[lang="mermaid"] .node text { font-size: 1rem; }
table tr th { border-bottom: 0px; }
video { max-width: 100%; display: block; margin: 0px auto; }
iframe { max-width: 100%; width: 100%; border: none; }
.highlight td, .highlight tr { border: 0px; }
mark { background: rgb(255, 255, 0); color: rgb(0, 0, 0); }
.md-html-inline .md-plain, .md-html-inline strong, mark .md-inline-math, mark strong { color: inherit; }
.md-expand mark .md-meta { opacity: 0.3 !important; }
mark .md-meta { color: rgb(0, 0, 0); }
@media print {
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}
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.md-diagram-panel .start-state { fill: var(--node-fill); }
.md-diagram-panel .edgeLabel rect { opacity: 1 !important; }
.md-fences.md-fences-math { font-size: 1em; }
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.outline-content strong { font-weight: 400; }
.outline-expander { width: 1rem; height: 1.42857rem; position: relative; display: table-cell; vertical-align: middle; cursor: pointer; padding-left: 4px; }
.outline-expander::before { content: ""; position: relative; font-family: Ionicons; display: inline-block; font-size: 8px; vertical-align: middle; }
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:root {
    --side-bar-bg-color: #fafafa;
    --control-text-color: #777;
}

@include-when-export url(https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext);

/* open-sans-regular - latin-ext_latin */
  /* open-sans-italic - latin-ext_latin */
    /* open-sans-700 - latin-ext_latin */
    /* open-sans-700italic - latin-ext_latin */
  html {
    font-size: 16px;
    -webkit-font-smoothing: antialiased;
}

body {
    font-family: "Open Sans","Clear Sans", "Helvetica Neue", Helvetica, Arial, 'Segoe UI Emoji', sans-serif;
    color: rgb(51, 51, 51);
    line-height: 1.6;
}

#write {
    max-width: 860px;
  	margin: 0 auto;
  	padding: 30px;
    padding-bottom: 100px;
}

@media only screen and (min-width: 1400px) {
	#write {
		max-width: 1024px;
	}
}

@media only screen and (min-width: 1800px) {
	#write {
		max-width: 1200px;
	}
}

#write > ul:first-child,
#write > ol:first-child{
    margin-top: 30px;
}

a {
    color: #4183C4;
}
h1,
h2,
h3,
h4,
h5,
h6 {
    position: relative;
    margin-top: 1rem;
    margin-bottom: 1rem;
    font-weight: bold;
    line-height: 1.4;
    cursor: text;
}
h1:hover a.anchor,
h2:hover a.anchor,
h3:hover a.anchor,
h4:hover a.anchor,
h5:hover a.anchor,
h6:hover a.anchor {
    text-decoration: none;
}
h1 tt,
h1 code {
    font-size: inherit;
}
h2 tt,
h2 code {
    font-size: inherit;
}
h3 tt,
h3 code {
    font-size: inherit;
}
h4 tt,
h4 code {
    font-size: inherit;
}
h5 tt,
h5 code {
    font-size: inherit;
}
h6 tt,
h6 code {
    font-size: inherit;
}
h1 {
    font-size: 2.25em;
    line-height: 1.2;
    border-bottom: 1px solid #eee;
}
h2 {
    font-size: 1.75em;
    line-height: 1.225;
    border-bottom: 1px solid #eee;
}

/*@media print {
    .typora-export h1,
    .typora-export h2 {
        border-bottom: none;
        padding-bottom: initial;
    }

    .typora-export h1::after,
    .typora-export h2::after {
        content: "";
        display: block;
        height: 100px;
        margin-top: -96px;
        border-top: 1px solid #eee;
    }
}*/

h3 {
    font-size: 1.5em;
    line-height: 1.43;
}
h4 {
    font-size: 1.25em;
}
h5 {
    font-size: 1em;
}
h6 {
   font-size: 1em;
    color: #777;
}
p,
blockquote,
ul,
ol,
dl,
table{
    margin: 0.8em 0;
}
li>ol,
li>ul {
    margin: 0 0;
}
hr {
    height: 2px;
    padding: 0;
    margin: 16px 0;
    background-color: #e7e7e7;
    border: 0 none;
    overflow: hidden;
    box-sizing: content-box;
}

li p.first {
    display: inline-block;
}
ul,
ol {
    padding-left: 30px;
}
ul:first-child,
ol:first-child {
    margin-top: 0;
}
ul:last-child,
ol:last-child {
    margin-bottom: 0;
}
blockquote {
    border-left: 4px solid #dfe2e5;
    padding: 0 15px;
    color: #777777;
}
blockquote blockquote {
    padding-right: 0;
}
table {
    padding: 0;
    word-break: initial;
}
table tr {
    border: 1px solid #dfe2e5;
    margin: 0;
    padding: 0;
}
table tr:nth-child(2n),
thead {
    background-color: #f8f8f8;
}
table th {
    font-weight: bold;
    border: 1px solid #dfe2e5;
    border-bottom: 0;
    margin: 0;
    padding: 6px 13px;
}
table td {
    border: 1px solid #dfe2e5;
    margin: 0;
    padding: 6px 13px;
}
table th:first-child,
table td:first-child {
    margin-top: 0;
}
table th:last-child,
table td:last-child {
    margin-bottom: 0;
}

.CodeMirror-lines {
    padding-left: 4px;
}

.code-tooltip {
    box-shadow: 0 1px 1px 0 rgba(0,28,36,.3);
    border-top: 1px solid #eef2f2;
}

.md-fences,
code,
tt {
    border: 1px solid #e7eaed;
    background-color: #f8f8f8;
    border-radius: 3px;
    padding: 0;
    padding: 2px 4px 0px 4px;
    font-size: 0.9em;
}

code {
    background-color: #f3f4f4;
    padding: 0 2px 0 2px;
}

.md-fences {
    margin-bottom: 15px;
    margin-top: 15px;
    padding-top: 8px;
    padding-bottom: 6px;
}


.md-task-list-item > input {
  margin-left: -1.3em;
}

@media print {
    html {
        font-size: 13px;
    }
    table,
    pre {
        page-break-inside: avoid;
    }
    pre {
        word-wrap: break-word;
    }
}

.md-fences {
	background-color: #f8f8f8;
}
#write pre.md-meta-block {
	padding: 1rem;
    font-size: 85%;
    line-height: 1.45;
    background-color: #f7f7f7;
    border: 0;
    border-radius: 3px;
    color: #777777;
    margin-top: 0 !important;
}

.mathjax-block>.code-tooltip {
	bottom: .375rem;
}

.md-mathjax-midline {
    background: #fafafa;
}

#write>h3.md-focus:before{
	left: -1.5625rem;
	top: .375rem;
}
#write>h4.md-focus:before{
	left: -1.5625rem;
	top: .285714286rem;
}
#write>h5.md-focus:before{
	left: -1.5625rem;
	top: .285714286rem;
}
#write>h6.md-focus:before{
	left: -1.5625rem;
	top: .285714286rem;
}
.md-image>.md-meta {
    /*border: 1px solid #ddd;*/
    border-radius: 3px;
    padding: 2px 0px 0px 4px;
    font-size: 0.9em;
    color: inherit;
}

.md-tag {
    color: #a7a7a7;
    opacity: 1;
}

.md-toc { 
    margin-top:20px;
    padding-bottom:20px;
}

.sidebar-tabs {
    border-bottom: none;
}

#typora-quick-open {
    border: 1px solid #ddd;
    background-color: #f8f8f8;
}

#typora-quick-open-item {
    background-color: #FAFAFA;
    border-color: #FEFEFE #e5e5e5 #e5e5e5 #eee;
    border-style: solid;
    border-width: 1px;
}

/** focus mode */
.on-focus-mode blockquote {
    border-left-color: rgba(85, 85, 85, 0.12);
}

header, .context-menu, .megamenu-content, footer{
    font-family: "Segoe UI", "Arial", sans-serif;
}

.file-node-content:hover .file-node-icon,
.file-node-content:hover .file-node-open-state{
    visibility: visible;
}

.mac-seamless-mode #typora-sidebar {
    background-color: #fafafa;
    background-color: var(--side-bar-bg-color);
}

.md-lang {
    color: #b4654d;
}

/*.html-for-mac {
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<body class='typora-export os-windows'><div class='typora-export-content'>
<div id='write'  class=''><p><span>在 4.1 节、我们已经得到、在非正则点附近，至少有一个解有本性奇点.对于二阶以上的方程来说、还有一个解可能是形式上的Frobenius 型级数但它往往是发散的）（见例 4.1.6）.我们要给出二阶方程具有形式上 Frobenius 型级数解的条件.</span></p><h2 id='定理一-对于\n∞\n-是非正则奇点的二阶常微分方程'><span>定理一: 对于</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.262ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 1000 453" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-126-TEX-N-221E" d="M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 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data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>x</mi></mfrac><mo>+</mo><mo>⋯</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd><mtd><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><blockquote><p><span>回顾正则情况</span></p><p><img src="https://gitee.com/wen-mingzhai/pic/raw/master/20211118154509.png" width="700px" /></p><p><span>非正则就是不满足，</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.254ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 3648.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: 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265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-52-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-52-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-52-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3E" xlink:href="#MJX-52-TEX-N-3E"></use></g><g data-mml-node="mo" transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-52-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="31" xlink:href="#MJX-52-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>&gt;</mo><mo>−</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1>-1</script><span>或</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.254ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 3648.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-53-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-53-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-53-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-53-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-53-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-53-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3E" xlink:href="#MJX-53-TEX-N-3E"></use></g><g data-mml-node="mo" transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-53-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="32" xlink:href="#MJX-53-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>&gt;</mo><mo>−</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_2>-2</script><span>。</span></p><p><span>例</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="17.513ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 7740.9 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-42-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-42-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-42-TEX-N-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path id="MJX-42-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-42-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-42-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-42-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-42-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-42-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3C" xlink:href="#MJX-42-TEX-N-3C"></use></g><g data-mml-node="mo" transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-42-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="31" xlink:href="#MJX-42-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3648.1,0)"><use data-c="2C" xlink:href="#MJX-42-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(4092.8,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-42-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-42-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(5407.1,0)"><use data-c="3D" xlink:href="#MJX-42-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(6462.9,0)"><use data-c="2212" xlink:href="#MJX-42-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(7240.9,0)"><use data-c="32" xlink:href="#MJX-42-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>&lt;</mo><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>n</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1<-1,n_1=-2</script><span>，多出来的</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.911ex" height="2.755ex" role="img" focusable="false" viewBox="0 -864.9 844.5 1217.7" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.798ex;"><defs><path id="MJX-43-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-43-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(245.5,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-43-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D465" xlink:href="#MJX-43-TEX-I-1D465"></use></g><rect width="604.5" height="60" x="120" y="220"></rect></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac></math></mjx-assistive-mml></mjx-container><script type="math/tex">\frac 1 x</script><span>可以放到括号里，相当于</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.274ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 2773.1 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-44-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-44-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-44-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-44-TEX-I-1D45D"></use></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-44-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(1217.3,0)"><use data-c="3D" xlink:href="#MJX-44-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2273.1,0)"><use data-c="30" xlink:href="#MJX-44-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>0</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p_0=0</script><span>，还是正则的形式</span></p></blockquote><p><span>该方程具有形式 Frobenius 型级数解的必要条件是</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n163" cid="n163" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-149-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-149-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-149-TEX-N-2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-149-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-149-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-149-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-149-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="2265" xlink:href="#MJX-149-TEX-N-2265"></use></g><g data-mml-node="msub" transform="translate(2370.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-149-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-149-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(3628.9,0)"><use data-c="2B" xlink:href="#MJX-149-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(4629.1,0)"><use data-c="31" xlink:href="#MJX-149-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>≥</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>+</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container></div></div><h3 id='证明'><span>证明:</span></h3><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n165" cid="n165" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" width="full" style="min-width: 35.711ex; position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="100%" height="6.399ex" role="img" focusable="false" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -2.634ex; min-width: 35.711ex;"><defs><path id="MJX-150-TEX-I-1D466" d="M21 287Q21 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mathvariant="normal">∞</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\infty</script><span> 处是非正则奇点, 所以有 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.254ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 3648.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-47-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 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data-c="7D" xlink:href="#MJX-152-TEX-N-7D"></use></g><g data-mml-node="mo" transform="translate(14151.9,0)"><use data-c="3D" xlink:href="#MJX-152-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(15207.7,0)"><use data-c="30" xlink:href="#MJX-152-TEX-N-30"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="left" columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>L</mi><mi>y</mi><mo>=</mo><msup><mi>y</mi><mo data-mjx-alternate="1">″</mo></msup><mo>+</mo><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><msup><mi>y</mi><mo data-mjx-alternate="1">′</mo></msup><mo>+</mo><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><msup><mi>y</mi><mo data-mjx-alternate="1">″</mo></msup><mo>=</mo><mo stretchy="false">(</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi><mo>−</mo><mi>k</mi></mrow></msup><msup><mo stretchy="false">)</mo><mo data-mjx-alternate="1">″</mo></msup><mo>=</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd><msup><mi>y</mi><mo data-mjx-alternate="1">′</mo></msup><mo>=</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo stretchy="false">)</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi></mrow></msup></mtd></mtr><mtr><mtd><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>x</mi></mfrac><mo>+</mo><mo>⋯</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd><mtd><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>x</mi></mfrac><mo>+</mo><mo>⋯</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd><mtd><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>∴</mo><mi>L</mi><mi>y</mi><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>r</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>p</mi><mi>r</mi></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mi>r</mi></mrow></msup><mo>⋅</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo stretchy="false">)</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle><mo>+</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>s</mi><mo>+</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>q</mi><mi>s</mi></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mi>s</mi></mrow></msup><mo>⋅</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi></mrow></msup></mtd></mtr><mtr><mtd><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>α</mi></mrow></msup><mo fence="false" stretchy="false">{</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>r</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>p</mi><mi>r</mi></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mi>r</mi></mrow></msup><mo>⋅</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mo stretchy="false">(</mo><mi>α</mi><mo>−</mo><mi>k</mi><mo stretchy="false">)</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle><mo>+</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>s</mi><mo>+</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>q</mi><mi>s</mi></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mi>s</mi></mrow></msup><mo>⋅</mo><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi></mrow></msup><mo fence="false" stretchy="false">}</mo><mo>=</mo><mn>0</mn></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>①第一项x幂次：-2,-3，-4，...</span></p><p><span>②第二项x幂次</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="13.973ex" height="1.91ex" role="img" focusable="false" viewBox="0 -694 6175.9 844" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-49-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-49-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-49-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-49-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-49-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-49-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-49-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-49-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(2259,0)"><use data-c="1D45F" xlink:href="#MJX-49-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2932.2,0)"><use data-c="2212" xlink:href="#MJX-49-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(3932.4,0)"><use data-c="1D458" xlink:href="#MJX-49-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(4675.7,0)"><use data-c="2212" xlink:href="#MJX-49-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(5675.9,0)"><use data-c="31" xlink:href="#MJX-49-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mi>r</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-r-k-1</script><span>:</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="24.396ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 10783 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-87-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-87-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-87-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-87-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-87-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-87-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-87-TEX-N-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-87-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-87-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-87-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-87-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(2759,0)"><use data-c="2C" xlink:href="#MJX-87-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(3203.7,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-87-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-87-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(4462.4,0)"><use data-c="2212" xlink:href="#MJX-87-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(5462.7,0)"><use data-c="32" xlink:href="#MJX-87-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(5962.7,0)"><use data-c="2C" xlink:href="#MJX-87-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(6407.3,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-87-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-87-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(7666.1,0)"><use data-c="2212" xlink:href="#MJX-87-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(8666.3,0)"><use data-c="33" xlink:href="#MJX-87-TEX-N-33"></use></g><g data-mml-node="mo" transform="translate(9166.3,0)"><use data-c="2C" xlink:href="#MJX-87-TEX-N-2C"></use></g><g data-mml-node="mo" transform="translate(9611,0)"><use data-c="2026" xlink:href="#MJX-87-TEX-N-2026"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>2</mn><mo>,</mo><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>3</mn><mo>,</mo><mo>…</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1,n_1-2,n_1-3,\dots</script></p><p><span>③第三项x幂次</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="32.501ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 14365.5 888" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-51-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-51-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-51-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-51-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-51-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-51-TEX-N-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-51-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-51-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 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xlink:href="#MJX-51-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(3950.4,0)"><use data-c="1D458" xlink:href="#MJX-51-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(4749.2,0)"><use data-c="3A" xlink:href="#MJX-51-TEX-N-3A"></use></g><g data-mml-node="msub" transform="translate(5305,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-51-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-51-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(6341.6,0)"><use data-c="2C" xlink:href="#MJX-51-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(6786.2,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-51-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-51-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(8045,0)"><use data-c="2212" xlink:href="#MJX-51-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(9045.2,0)"><use data-c="31" xlink:href="#MJX-51-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(9545.2,0)"><use data-c="2C" xlink:href="#MJX-51-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(9989.9,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-51-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-51-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(11248.7,0)"><use data-c="2212" xlink:href="#MJX-51-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(12248.9,0)"><use data-c="32" xlink:href="#MJX-51-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(12748.9,0)"><use data-c="2C" xlink:href="#MJX-51-TEX-N-2C"></use></g><g data-mml-node="mo" transform="translate(13193.5,0)"><use data-c="2026" xlink:href="#MJX-51-TEX-N-2026"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mi>s</mi><mo>−</mo><mi>k</mi><mo>:</mo><msub><mi>n</mi><mn>2</mn></msub><mo>,</mo><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mn>2</mn><mo>,</mo><mo>…</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_2-s-k:n_2,n_2-1,n_2-2,\dots</script></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.254ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 3648.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-52-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-52-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-52-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-52-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-52-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-52-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3E" xlink:href="#MJX-52-TEX-N-3E"></use></g><g data-mml-node="mo" transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-52-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="31" xlink:href="#MJX-52-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>&gt;</mo><mo>−</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1>-1</script><span>或</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.254ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 3648.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-53-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-53-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-53-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-53-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-53-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-53-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3E" xlink:href="#MJX-53-TEX-N-3E"></use></g><g data-mml-node="mo" transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-53-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="32" xlink:href="#MJX-53-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>&gt;</mo><mo>−</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_2>-2</script><span>。</span></p><p><span>①②③之和的首项的次幂：-2+</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.353ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5018 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-54-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-54-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-54-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-54-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-54-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-54-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-54-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-54-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-54-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(2981.2,0)"><use data-c="2B" xlink:href="#MJX-54-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(3981.4,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-54-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-54-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>+</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1+n_2</script></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="22.404ex" height="2.149ex" role="img" focusable="false" viewBox="0 -750 9902.7 950" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.452ex;"><defs><path id="MJX-55-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-55-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-55-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-55-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-55-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-55-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-55-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-55-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-55-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3E" xlink:href="#MJX-55-TEX-N-3E"></use></g><g data-mml-node="mo" transform="translate(4092.6,0)"><use data-c="2212" xlink:href="#MJX-55-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(4870.6,0)"><use data-c="32" xlink:href="#MJX-55-TEX-N-32"></use></g><g data-mml-node="mtext" transform="translate(5370.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">或</text></g><g data-mml-node="msub" transform="translate(6254.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-55-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-55-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(7568.9,0)"><use data-c="3E" xlink:href="#MJX-55-TEX-N-3E"></use></g><g data-mml-node="mo" transform="translate(8624.7,0)"><use data-c="2212" xlink:href="#MJX-55-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(9402.7,0)"><use data-c="32" xlink:href="#MJX-55-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>&gt;</mo><mo>−</mo><mn>2</mn><mtext>或</mtext><msub><mi>n</mi><mn>2</mn></msub><mo>&gt;</mo><mo>−</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1>-2或n_2>-2</script></p><p><span>首项并不平衡</span></p><p><img src="https://gitee.com/wen-mingzhai/pic/raw/master/E702B0B6-4972-4D76-9513-0D76027367D6(1).png" width="300px" /></p><ul><li><span>若</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.748ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5192.6 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-56-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-56-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-56-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-56-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-56-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-56-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-56-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-56-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-56-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3D" xlink:href="#MJX-56-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(4092.6,0)"><use data-c="1D45B" xlink:href="#MJX-56-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(4692.6,0)"><use data-c="32" xlink:href="#MJX-56-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>=</mo><mi>n</mi><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1=n2</script><span>，则首项由②③贡献</span></li></ul><p><span>首项的系数为零：</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="16.419ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 7257.2 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-94-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-94-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-94-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-94-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-94-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-94-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-94-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-94-TEX-I-1D45D"></use></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-94-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(939.6,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-94-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-94-TEX-N-30"></use></g></g><g data-mml-node="mi" transform="translate(1809.1,0)"><use data-c="1D6FC" xlink:href="#MJX-94-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(2671.3,0)"><use data-c="2B" xlink:href="#MJX-94-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(3671.6,0)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-94-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-94-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(4554.1,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-94-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-94-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(5701.4,0)"><use data-c="3D" xlink:href="#MJX-94-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(6757.2,0)"><use data-c="30" xlink:href="#MJX-94-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mi>α</mi><mo>+</mo><msub><mi>q</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p_0c_0\alpha+q_0c_0=0</script><span>，即</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.484ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 5518.1 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-58-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 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transform="translate(1801.8,0)"><use data-c="2B" xlink:href="#MJX-58-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(2802,0)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-58-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-58-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(3962.3,0)"><use data-c="3D" xlink:href="#MJX-58-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(5018.1,0)"><use data-c="30" xlink:href="#MJX-58-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>0</mn></msub><mi>α</mi><mo>+</mo><msub><mi>q</mi><mn>0</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p_0\alpha+q_0=0</script><span>,即</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.724ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 3855.9 1271.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.091ex;"><defs><path id="MJX-95-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-95-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-95-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-95-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-95-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 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data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-95-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-95-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1973.6,0)"><use data-c="2212" xlink:href="#MJX-95-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2751.6,0)"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-95-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-95-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(220,-345) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-95-TEX-I-1D45D"></use></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-95-TEX-N-30"></use></g></g><rect width="864.4" height="60" x="120" y="220"></rect></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mo>−</mo><mfrac><msub><mi>q</mi><mn>0</mn></msub><msub><mi>p</mi><mn>0</mn></msub></mfrac></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha=-\frac{q_0}{p_0}</script></p><ul><li><p><span>若</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-96-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-96-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-96-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-96-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-96-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-96-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-96-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-96-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-96-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3E" xlink:href="#MJX-96-TEX-N-3E"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-96-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-96-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>&gt;</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1>n_2</script><span>,则首项由②贡献</span></p><p><span>首项的系数为零：</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="9.689ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 4282.7 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-91-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-91-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-91-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-91-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-91-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-91-TEX-I-1D45D"></use></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-91-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(939.6,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-91-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-91-TEX-N-30"></use></g></g><g data-mml-node="mi" transform="translate(1809.1,0)"><use data-c="1D6FC" xlink:href="#MJX-91-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(2726.9,0)"><use data-c="3D" xlink:href="#MJX-91-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(3782.7,0)"><use data-c="30" xlink:href="#MJX-91-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p_0c_0\alpha=0</script><span>,即</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.596ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2473.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-109-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-109-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-109-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-109-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-109-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1973.6,0)"><use data-c="30" xlink:href="#MJX-109-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha=0</script></p></li><li><p><span>若</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-90-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-90-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-90-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-90-TEX-N-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path id="MJX-90-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-90-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-90-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-90-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-90-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3C" xlink:href="#MJX-90-TEX-N-3C"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-90-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-90-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>&lt;</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1<n_2</script><span>,则首项由③贡献</span></p></li></ul><p><span>        首项的系数为零：</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.112ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 3585.7 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-97-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-97-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-97-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-97-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-97-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-97-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(882.6,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-97-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-97-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(2029.9,0)"><use data-c="3D" xlink:href="#MJX-97-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(3085.7,0)"><use data-c="30" xlink:href="#MJX-97-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">q_0c_0=0</script><span>,不成立</span></p><p><span>所以，</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-65-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-65-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-65-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-65-TEX-N-2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-65-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-65-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-65-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-65-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-65-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="2265" xlink:href="#MJX-65-TEX-N-2265"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-65-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-65-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>≥</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1\ge n_2</script><span>时，有Froubenius级数解。（中间的梯子是最高的或最高的之一）</span></p></blockquote><p><span>我们要求同次幂项等于零. </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="3.526ex" height="1.912ex" role="img" focusable="false" viewBox="0 -833.9 1558.7 844.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-66-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-66-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-66-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-66-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2212" xlink:href="#MJX-66-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(778,0)"><use data-c="31" xlink:href="#MJX-66-TEX-N-31"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></msup></math></mjx-assistive-mml></mjx-container><script type="math/tex">x^{-1}</script><span> 的最低次幂项必在后面两个和式中 出现. 若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="7.707ex" height="1.778ex" role="img" focusable="false" viewBox="0 -636 3406.7 786" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-67-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-67-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-67-TEX-N-2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-67-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-67-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-67-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="2265" xlink:href="#MJX-67-TEX-N-2265"></use></g><g data-mml-node="msub" transform="translate(2370.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-67-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-67-TEX-N-31"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>≥</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_{2} \geq n_{1}</script><span>, 得</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n192" cid="n192" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.116ex" height="1.881ex" role="img" focusable="false" viewBox="0 -666 2703.1 831.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-153-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-153-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-153-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-153-TEX-I-1D450"></use></g><g data-mml-node="TeXAtom" transform="translate(466,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-153-TEX-N-30"></use></g></g></g><g data-mml-node="mo" transform="translate(1147.3,0)"><use data-c="3D" xlink:href="#MJX-153-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2203.1,0)"><use data-c="30" xlink:href="#MJX-153-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>与原先假设式盾.</span>
<span>若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-68-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-68-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-68-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-68-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-68-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-68-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-68-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2B" xlink:href="#MJX-68-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-68-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3D" xlink:href="#MJX-68-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-68-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-68-TEX-N-31"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>+</mo><mn>1</mn><mo>=</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_{2}+1=n_{1}</script><span>, 得</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n194" cid="n194" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.484ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 5518.1 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-154-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-154-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-154-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-154-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-154-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-154-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-154-TEX-I-1D45E"></use></g><g data-mml-node="TeXAtom" transform="translate(479,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-154-TEX-N-30"></use></g></g></g><g data-mml-node="mo" transform="translate(1104.8,0)"><use data-c="2B" xlink:href="#MJX-154-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(2105,0)"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-154-TEX-I-1D45D"></use></g><g data-mml-node="TeXAtom" transform="translate(536,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-154-TEX-N-30"></use></g></g></g><g data-mml-node="mi" transform="translate(3044.6,0)"><use data-c="1D6FC" xlink:href="#MJX-154-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(3962.3,0)"><use data-c="3D" xlink:href="#MJX-154-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(5018.1,0)"><use data-c="30" xlink:href="#MJX-154-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>所以, 特征指数为</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n196" cid="n196" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="9.346ex" height="4.52ex" role="img" focusable="false" viewBox="0 -1118 4131.1 1998" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.991ex;"><defs><path id="MJX-155-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-155-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-155-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-155-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-155-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-155-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-155-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-155-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1973.6,0)"><use data-c="2212" xlink:href="#MJX-155-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2751.6,0)"><g data-mml-node="msub" transform="translate(248.5,676)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-155-TEX-I-1D45E"></use></g><g data-mml-node="TeXAtom" transform="translate(479,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-155-TEX-N-30"></use></g></g></g><g data-mml-node="msub" transform="translate(220,-686)"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-155-TEX-I-1D45D"></use></g><g data-mml-node="TeXAtom" transform="translate(536,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-155-TEX-N-30"></use></g></g></g><rect width="1139.6" height="60" x="120" y="220"></rect></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>α</mi><mo>=</mo><mo>−</mo><mfrac><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mfrac></math></mjx-assistive-mml></mjx-container></div></div><p><span>若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-69-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-69-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-69-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-69-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-69-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-69-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-69-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3E" xlink:href="#MJX-69-TEX-N-3E"></use></g><g data-mml-node="msub" transform="translate(2370.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-69-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-69-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(3628.9,0)"><use data-c="2B" xlink:href="#MJX-69-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(4629.1,0)"><use data-c="31" xlink:href="#MJX-69-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>&gt;</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>+</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_{1}>n_{2}+1</script><span> ：得</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n198" cid="n198" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.596ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2473.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-156-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-156-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-156-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-156-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-156-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1973.6,0)"><use data-c="30" xlink:href="#MJX-156-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>然后再推出递推公式.</span>
<span>这里, 我们还要考虑 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.341ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3686.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-104-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-104-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-104-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-104-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-104-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-104-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-104-TEX-I-1D45D"></use></g><g data-mml-node="mo" transform="translate(503,0)"><use data-c="28" xlink:href="#MJX-104-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(892,0)"><use data-c="1D465" xlink:href="#MJX-104-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1464,0)"><use data-c="29" xlink:href="#MJX-104-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2130.8,0)"><use data-c="2261" xlink:href="#MJX-104-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(3186.6,0)"><use data-c="30" xlink:href="#MJX-104-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p(x) \equiv 0</script><span> 或 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.243ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3643.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-105-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 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type="math/tex">q(x) \equiv 0</script><span> 的情况 (但不能全 等于零, 因为 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.574ex" height="1.505ex" role="img" focusable="false" viewBox="0 -583 2905.6 665" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-72-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 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xlink:href="#MJX-72-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(849.8,0)"><use data-c="3D" xlink:href="#MJX-72-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(1905.6,0)"><use data-c="221E" xlink:href="#MJX-72-TEX-N-221E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi mathvariant="normal">∞</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">x=\infty</script><span> 是非正则合点), 若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.286ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 2336.6 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-106-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-106-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-106-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-106-TEX-I-1D45D"></use></g><g data-mml-node="mo" transform="translate(780.8,0)"><use data-c="2261" xlink:href="#MJX-106-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(1836.6,0)"><use data-c="30" xlink:href="#MJX-106-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p \equiv 0</script><span> 得 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.116ex" height="1.881ex" role="img" focusable="false" viewBox="0 -666 2703.1 831.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-107-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-107-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 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data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">c_{0}=0</script><span>, 与假设矛盾. 若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.189ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 2293.6 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-75-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-75-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-75-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-75-TEX-I-1D45E"></use></g><g data-mml-node="mo" transform="translate(737.8,0)"><use data-c="2261" xlink:href="#MJX-75-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(1793.6,0)"><use data-c="30" xlink:href="#MJX-75-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">q \equiv 0</script><span>, 得 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.596ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2473.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-109-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-109-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-109-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" 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395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-104-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-104-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 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data-mjx-texclass="CLOSE">)</mo></mrow><mo>,</mo></mtd><mtd><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>x</mi><mo>+</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>,</mo></mtd><mtd><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>在 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.442ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2405.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-83-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-83-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-83-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-83-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(849.8,0)"><use data-c="3D" xlink:href="#MJX-83-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1905.6,0)"><use data-c="30" xlink:href="#MJX-83-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">x=0</script><span> 处有正则解的必要条件为</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n207" cid="n207" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-159-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-159-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-159-TEX-N-2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-159-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-159-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-159-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-159-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="2264" xlink:href="#MJX-159-TEX-N-2264"></use></g><g data-mml-node="msub" transform="translate(2370.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-159-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-159-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(3628.9,0)"><use data-c="2B" xlink:href="#MJX-159-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(4629.1,0)"><use data-c="31" xlink:href="#MJX-159-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>≤</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>+</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container></div></div><blockquote><p><span>回顾：非正则奇点的条件</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="18.507ex" height="2.149ex" role="img" focusable="false" viewBox="0 -750 8180.2 950" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.452ex;"><defs><path id="MJX-89-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-89-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-89-TEX-N-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path id="MJX-89-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path 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transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-89-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="31" xlink:href="#MJX-89-TEX-N-31"></use></g><g data-mml-node="mtext" transform="translate(3648.1,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">或</text></g><g data-mml-node="msub" transform="translate(4532.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-89-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-89-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(5846.4,0)"><use data-c="3C" xlink:href="#MJX-89-TEX-N-3C"></use></g><g data-mml-node="mo" transform="translate(6902.2,0)"><use data-c="2212" xlink:href="#MJX-89-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(7680.2,0)"><use data-c="32" xlink:href="#MJX-89-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>&lt;</mo><mo>−</mo><mn>1</mn><mtext>或</mtext><msub><mi>n</mi><mn>2</mn></msub><mo>&lt;</mo><mo>−</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1<-1或n_2<-2</script></p></blockquote><h3 id='证明-同样可假定'><span>证明, 同样可假定</span></h3><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n211" cid="n211" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="18.023ex" height="6.399ex" role="img" focusable="false" viewBox="0 -1562.5 7966.2 2828.3" 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transform="translate(5462.7,0)"><use data-c="32" xlink:href="#MJX-87-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(5962.7,0)"><use data-c="2C" xlink:href="#MJX-87-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(6407.3,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-87-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-87-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(7666.1,0)"><use data-c="2212" xlink:href="#MJX-87-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(8666.3,0)"><use data-c="33" xlink:href="#MJX-87-TEX-N-33"></use></g><g data-mml-node="mo" transform="translate(9166.3,0)"><use data-c="2C" xlink:href="#MJX-87-TEX-N-2C"></use></g><g data-mml-node="mo" transform="translate(9611,0)"><use data-c="2026" xlink:href="#MJX-87-TEX-N-2026"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>2</mn><mo>,</mo><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>3</mn><mo>,</mo><mo>…</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1,n_1-2,n_1-3,\dots</script></p><p><span>③第三项x幂次</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="32.501ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 14365.5 888" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-88-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-88-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-88-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-88-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-88-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-88-TEX-N-3A" d="M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-88-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path id="MJX-88-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-88-TEX-N-31" d="M213 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xlink:href="#MJX-88-TEX-N-2B"></use></g><g data-mml-node="mi" transform="translate(2259,0)"><use data-c="1D460" xlink:href="#MJX-88-TEX-I-1D460"></use></g><g data-mml-node="mo" transform="translate(2950.2,0)"><use data-c="2B" xlink:href="#MJX-88-TEX-N-2B"></use></g><g data-mml-node="mi" transform="translate(3950.4,0)"><use data-c="1D458" xlink:href="#MJX-88-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(4749.2,0)"><use data-c="3A" xlink:href="#MJX-88-TEX-N-3A"></use></g><g data-mml-node="msub" transform="translate(5305,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-88-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-88-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(6341.6,0)"><use data-c="2C" xlink:href="#MJX-88-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(6786.2,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-88-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-88-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(8045,0)"><use data-c="2212" xlink:href="#MJX-88-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(9045.2,0)"><use data-c="31" xlink:href="#MJX-88-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(9545.2,0)"><use data-c="2C" xlink:href="#MJX-88-TEX-N-2C"></use></g><g data-mml-node="msub" transform="translate(9989.9,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-88-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-88-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(11248.7,0)"><use data-c="2212" xlink:href="#MJX-88-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(12248.9,0)"><use data-c="32" xlink:href="#MJX-88-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(12748.9,0)"><use data-c="2C" xlink:href="#MJX-88-TEX-N-2C"></use></g><g data-mml-node="mo" transform="translate(13193.5,0)"><use data-c="2026" xlink:href="#MJX-88-TEX-N-2026"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>+</mo><mi>s</mi><mo>+</mo><mi>k</mi><mo>:</mo><msub><mi>n</mi><mn>2</mn></msub><mo>,</mo><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mn>1</mn><mo>,</mo><msub><mi>n</mi><mn>2</mn></msub><mo>−</mo><mn>2</mn><mo>,</mo><mo>…</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_2+s+k:n_2,n_2-1,n_2-2,\dots</script></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="18.507ex" height="2.149ex" role="img" focusable="false" viewBox="0 -750 8180.2 950" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.452ex;"><defs><path id="MJX-89-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-89-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-89-TEX-N-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path id="MJX-89-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-89-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-89-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-89-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3C" xlink:href="#MJX-89-TEX-N-3C"></use></g><g data-mml-node="mo" transform="translate(2370.1,0)"><use data-c="2212" xlink:href="#MJX-89-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(3148.1,0)"><use data-c="31" xlink:href="#MJX-89-TEX-N-31"></use></g><g data-mml-node="mtext" transform="translate(3648.1,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">或</text></g><g data-mml-node="msub" transform="translate(4532.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-89-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-89-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(5846.4,0)"><use data-c="3C" xlink:href="#MJX-89-TEX-N-3C"></use></g><g data-mml-node="mo" transform="translate(6902.2,0)"><use data-c="2212" xlink:href="#MJX-89-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(7680.2,0)"><use data-c="32" xlink:href="#MJX-89-TEX-N-32"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>&lt;</mo><mo>−</mo><mn>1</mn><mtext>或</mtext><msub><mi>n</mi><mn>2</mn></msub><mo>&lt;</mo><mo>−</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1<-1或n_2<-2</script><span>，</span></p><p><img src="https://gitee.com/wen-mingzhai/pic/raw/master/BD1D1B0D-DEF6-4870-A200-C24E01BC996D(1).png" width="300px" /></p><p><span>第二三个梯子仍比第一个高。</span></p><ul><li><span>若</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-90-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-90-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-90-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-90-TEX-N-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path id="MJX-90-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-90-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-90-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-90-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-90-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3C" xlink:href="#MJX-90-TEX-N-3C"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-90-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-90-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>&lt;</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1<n_2</script><span>​,则首项由②贡献</span></li></ul><p><span>首项的系数为零:</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="9.689ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 4282.7 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-91-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 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255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-109-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-109-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-109-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-109-TEX-N-3D"></use></g><g data-mml-node="mn" 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386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-93-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-93-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-93-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-93-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 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xlink:href="#MJX-93-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-93-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-93-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>=</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1=n_2</script><span>​,则首项由②③贡献</span></li></ul><p><span>首项的系数为零:</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="16.419ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 7257.2 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-94-TEX-I-1D45D" 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xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mi>α</mi><mo>+</mo><msub><mi>q</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p_0c_0\alpha+q_0c_0=0</script><span>,</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.724ex" height="2.878ex" role="img" focusable="false" viewBox="0 -789.7 3855.9 1271.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.091ex;"><defs><path id="MJX-95-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-95-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-95-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-95-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 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316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-95-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-95-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1973.6,0)"><use data-c="2212" xlink:href="#MJX-95-TEX-N-2212"></use></g><g data-mml-node="mfrac" transform="translate(2751.6,0)"><g data-mml-node="msub" transform="translate(240.2,477.2) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-95-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-95-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(220,-345) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-95-TEX-I-1D45D"></use></g><g data-mml-node="mn" transform="translate(536,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-95-TEX-N-30"></use></g></g><rect width="864.4" height="60" x="120" y="220"></rect></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mo>−</mo><mfrac><msub><mi>q</mi><mn>0</mn></msub><msub><mi>p</mi><mn>0</mn></msub></mfrac></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha=-\frac{q_0}{p_0}</script></p><ul><li><span>若</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-96-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-96-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-96-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-96-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-96-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-96-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-96-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-96-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-96-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="3E" xlink:href="#MJX-96-TEX-N-3E"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-96-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-96-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>&gt;</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_1-1>n_2</script><span>​,则首项由③贡献</span></li></ul><p><span>首项的系数为零:</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.112ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 3585.7 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-97-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-97-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-97-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-97-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-97-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-97-TEX-N-30"></use></g></g><g data-mml-node="msub" transform="translate(882.6,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-97-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-97-TEX-N-30"></use></g></g><g data-mml-node="mo" transform="translate(2029.9,0)"><use data-c="3D" xlink:href="#MJX-97-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(3085.7,0)"><use data-c="30" xlink:href="#MJX-97-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>0</mn></msub><msub><mi>c</mi><mn>0</mn></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">q_0c_0=0</script><span>,不成立</span></p><p><span>所以</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-98-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-98-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-98-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-98-TEX-N-2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-98-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-98-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-98-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(1258.8,0)"><use data-c="2212" xlink:href="#MJX-98-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2259,0)"><use data-c="31" xlink:href="#MJX-98-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(3036.8,0)"><use data-c="2264" xlink:href="#MJX-98-TEX-N-2264"></use></g><g data-mml-node="msub" transform="translate(4092.6,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-98-TEX-I-1D45B"></use></g><g data-mml-node="mn" transform="translate(633,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-98-TEX-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>−</mo><mn>1</mn><mo>≤</mo><msub><mi>n</mi><mn>2</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex"> n_1-1\le n_2</script></p></blockquote><p><span>这时, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.294ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 572 453" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-99-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-99-TEX-I-1D465"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">x</script><span> 的最低次幂的项由后面两个乘积产生. 若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-100-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-100-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-100-TEX-N-3C" d="M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z"></path><path id="MJX-100-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-100-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-100-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-100-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3C" xlink:href="#MJX-100-TEX-N-3C"></use></g><g data-mml-node="msub" transform="translate(2370.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-100-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-100-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(3628.9,0)"><use data-c="2212" xlink:href="#MJX-100-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(4629.1,0)"><use data-c="31" xlink:href="#MJX-100-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>&lt;</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_{2}<n_{1}-1</script><span>, 要求</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n235" cid="n235" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.116ex" height="1.881ex" role="img" focusable="false" viewBox="0 -666 2703.1 831.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-162-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-162-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-162-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-162-TEX-I-1D450"></use></g><g data-mml-node="TeXAtom" transform="translate(466,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-162-TEX-N-30"></use></g></g></g><g data-mml-node="mo" transform="translate(1147.3,0)"><use data-c="3D" xlink:href="#MJX-162-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2203.1,0)"><use data-c="30" xlink:href="#MJX-162-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>与原假设矛盾</span>
<span>若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-101-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-101-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-101-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-101-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-101-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 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transform="translate(4629.1,0)"><use data-c="31" xlink:href="#MJX-101-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_{2}=n_{1}-1</script><span>, 要求</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n237" cid="n237" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.484ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 5518.1 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-163-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-163-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 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data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-163-TEX-I-1D45E"></use></g><g data-mml-node="TeXAtom" transform="translate(479,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-163-TEX-N-30"></use></g></g></g><g data-mml-node="mo" transform="translate(1104.8,0)"><use data-c="2B" xlink:href="#MJX-163-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(2105,0)"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-163-TEX-I-1D45D"></use></g><g data-mml-node="TeXAtom" transform="translate(536,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-163-TEX-N-30"></use></g></g></g><g data-mml-node="mi" transform="translate(3044.6,0)"><use data-c="1D6FC" xlink:href="#MJX-163-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(3962.3,0)"><use data-c="3D" xlink:href="#MJX-163-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(5018.1,0)"><use data-c="30" xlink:href="#MJX-163-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>特征指数</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n239" cid="n239" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="9.346ex" height="4.52ex" role="img" focusable="false" viewBox="0 -1118 4131.1 1998" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.991ex;"><defs><path id="MJX-164-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-164-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-164-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-164-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-164-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-164-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-164-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" 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xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>α</mi><mo>=</mo><mo>−</mo><mfrac><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mfrac></math></mjx-assistive-mml></mjx-container></div></div><p><span>若 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="11.604ex" height="1.846ex" role="img" focusable="false" viewBox="0 -666 5129.1 816" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-102-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-102-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-102-TEX-N-3E" d="M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z"></path><path id="MJX-102-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-102-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-102-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-102-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(1314.3,0)"><use data-c="3E" xlink:href="#MJX-102-TEX-N-3E"></use></g><g data-mml-node="msub" transform="translate(2370.1,0)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-102-TEX-I-1D45B"></use></g><g data-mml-node="TeXAtom" transform="translate(633,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-102-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(3628.9,0)"><use data-c="2212" xlink:href="#MJX-102-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(4629.1,0)"><use data-c="31" xlink:href="#MJX-102-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>&gt;</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n_{2}>n_{1}-1</script><span>, 得</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n241" cid="n241" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.596ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2473.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-165-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-165-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-165-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-165-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-165-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1973.6,0)"><use data-c="30" xlink:href="#MJX-165-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>即特征指数 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.448ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 640 453" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-103-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-103-TEX-I-1D6FC"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha</script><span> 为零.</span>
<span>这里还要讨论 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.341ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3686.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-104-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-104-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-104-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-104-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-104-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-104-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-104-TEX-I-1D45D"></use></g><g data-mml-node="mo" transform="translate(503,0)"><use data-c="28" xlink:href="#MJX-104-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(892,0)"><use data-c="1D465" xlink:href="#MJX-104-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1464,0)"><use data-c="29" xlink:href="#MJX-104-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2130.8,0)"><use data-c="2261" xlink:href="#MJX-104-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(3186.6,0)"><use data-c="30" xlink:href="#MJX-104-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p(x) \equiv 0</script><span> 或 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.243ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3643.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-105-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-105-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-105-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-105-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-105-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-105-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-105-TEX-I-1D45E"></use></g><g data-mml-node="mo" transform="translate(460,0)"><use data-c="28" xlink:href="#MJX-105-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(849,0)"><use data-c="1D465" xlink:href="#MJX-105-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1421,0)"><use data-c="29" xlink:href="#MJX-105-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2087.8,0)"><use data-c="2261" xlink:href="#MJX-105-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(3143.6,0)"><use data-c="30" xlink:href="#MJX-105-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">q(x) \equiv 0</script><span> 的情况 (但不能全等于零,因为这是非正则奇点). </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.286ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 2336.6 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-106-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-106-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-106-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-106-TEX-I-1D45D"></use></g><g data-mml-node="mo" transform="translate(780.8,0)"><use data-c="2261" xlink:href="#MJX-106-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(1836.6,0)"><use data-c="30" xlink:href="#MJX-106-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">p \equiv 0</script><span> 时, 要求 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.116ex" height="1.881ex" role="img" focusable="false" viewBox="0 -666 2703.1 831.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-107-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-107-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-107-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-107-TEX-I-1D450"></use></g><g data-mml-node="TeXAtom" transform="translate(466,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="30" xlink:href="#MJX-107-TEX-N-30"></use></g></g></g><g data-mml-node="mo" transform="translate(1147.3,0)"><use data-c="3D" xlink:href="#MJX-107-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2203.1,0)"><use data-c="30" xlink:href="#MJX-107-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">c_{0}=0</script><span>, 与假设矛盾. </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="7.451ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 3293.6 860" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-108-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-108-TEX-N-2261" d="M56 444Q56 457 70 464H707Q722 456 722 444Q722 430 706 424H72Q56 429 56 444ZM56 237T56 250T70 270H707Q722 262 722 250T707 230H70Q56 237 56 250ZM56 56Q56 71 72 76H706Q722 70 722 56Q722 44 707 36H70Q56 43 56 56Z"></path><path id="MJX-108-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mstyle"><g data-mml-node="mspace"></g></g><g data-mml-node="mi" transform="translate(1000,0)"><use data-c="1D45E" xlink:href="#MJX-108-TEX-I-1D45E"></use></g><g data-mml-node="mo" transform="translate(1737.8,0)"><use data-c="2261" xlink:href="#MJX-108-TEX-N-2261"></use></g><g data-mml-node="mn" transform="translate(2793.6,0)"><use data-c="30" xlink:href="#MJX-108-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle scriptlevel="0"><mspace width="1em"></mspace></mstyle><mi>q</mi><mo>≡</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">\quad q \equiv 0</script><span>时, 要求特征指数 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.596ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2473.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-109-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-109-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-109-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-109-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(917.8,0)"><use data-c="3D" xlink:href="#MJX-109-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(1973.6,0)"><use data-c="30" xlink:href="#MJX-109-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha=0</script><span>, 可以有 Frobenius 型的形式解.</span></p><blockquote><p><span>定理一二总结：第二个梯子要对首项有贡献，才会有Froubenius型级数解。</span></p></blockquote><blockquote><p><span>正则奇异点与非正则奇异点的区别：正则，三个梯子一样高，即对首项都有贡献。非正则不一样高，其中几个对首项有贡献。</span></p></blockquote><p><span>如果在非正则奇点附近, 系数 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="9.293ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4107.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-110-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-110-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-110-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-110-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path id="MJX-110-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 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transform="translate(503,0)"><use data-c="28" xlink:href="#MJX-110-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(892,0)"><use data-c="1D465" xlink:href="#MJX-110-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1464,0)"><use data-c="29" xlink:href="#MJX-110-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(1853,0)"><use data-c="2C" xlink:href="#MJX-110-TEX-N-2C"></use></g><g data-mml-node="mi" transform="translate(2297.7,0)"><use data-c="1D45E" xlink:href="#MJX-110-TEX-I-1D45E"></use></g><g data-mml-node="mo" transform="translate(2757.7,0)"><use data-c="28" xlink:href="#MJX-110-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(3146.7,0)"><use data-c="1D465" xlink:href="#MJX-110-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(3718.7,0)"><use data-c="29" xlink:href="#MJX-110-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">p(x), q(x)</script><span> 不满足定理一, 定理 二的条件</span></p><blockquote><p><span>也就不能写成Froubenius级数解形式</span></p></blockquote><p><span>, 我们可以求</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n251" cid="n251" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="18.076ex" height="2.7ex" role="img" focusable="false" viewBox="0 -943.3 7989.5 1193.3" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-166-TEX-I-1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-166-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 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43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D466" xlink:href="#MJX-166-TEX-I-1D466"></use></g><g data-mml-node="mo" transform="translate(490,0)"><use data-c="28" xlink:href="#MJX-166-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(879,0)"><use data-c="1D465" xlink:href="#MJX-166-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1451,0)"><use data-c="29" xlink:href="#MJX-166-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2117.8,0)"><use data-c="3D" xlink:href="#MJX-166-TEX-N-3D"></use></g><g data-mml-node="msup" transform="translate(3173.6,0)"><g data-mml-node="mi"><use data-c="1D452" xlink:href="#MJX-166-TEX-I-1D452"></use></g><g data-mml-node="TeXAtom" transform="translate(499,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-166-TEX-I-1D460"></use></g><g data-mml-node="mo" transform="translate(469,0)"><use data-c="28" xlink:href="#MJX-166-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(858,0)"><use data-c="1D465" xlink:href="#MJX-166-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1430,0)"><use data-c="29" xlink:href="#MJX-166-TEX-N-29"></use></g></g></g><g data-mml-node="msup" transform="translate(5008.8,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-166-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D70E" xlink:href="#MJX-166-TEX-I-1D70E"></use></g></g></g><g data-mml-node="mi" transform="translate(6067.5,0)"><use data-c="1D462" xlink:href="#MJX-166-TEX-I-1D462"></use></g><g data-mml-node="mo" transform="translate(6639.5,0)"><use data-c="28" xlink:href="#MJX-166-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(7028.5,0)"><use data-c="1D465" xlink:href="#MJX-166-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(7600.5,0)"><use data-c="29" xlink:href="#MJX-166-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></msup><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msup><mi>u</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container></div></div><p><span>形式的解. 在 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.262ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 1000 453" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-126-TEX-N-221E" d="M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="221E" xlink:href="#MJX-126-TEX-N-221E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∞</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\infty</script><span> 处, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.115ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1819 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-142-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-142-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-142-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-142-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-142-TEX-I-1D460"></use></g><g data-mml-node="mo" transform="translate(469,0)"><use data-c="28" xlink:href="#MJX-142-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(858,0)"><use data-c="1D465" xlink:href="#MJX-142-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1430,0)"><use data-c="29" xlink:href="#MJX-142-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">s(x)</script><span> 为 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.042ex" height="2.046ex" role="img" focusable="false" viewBox="0 -893.3 1786.4 904.3" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-113-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-113-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-113-TEX-N-2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path><path id="MJX-113-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-113-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="31" xlink:href="#MJX-113-TEX-N-31"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(500,0)"><g data-mml-node="mo"><use data-c="2F" xlink:href="#MJX-113-TEX-N-2F"></use></g></g><g data-mml-node="mi" transform="translate(1000,0)"><use data-c="1D45B" xlink:href="#MJX-113-TEX-I-1D45B"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn><mrow data-mjx-texclass="ORD"><mo>/</mo></mrow><mi>n</mi></mrow></msup></math></mjx-assistive-mml></mjx-container><script type="math/tex">x^{1 / n}</script><span> 的正次幂多项式. </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.348ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1922 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-118-TEX-I-1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-118-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-118-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-118-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D462" xlink:href="#MJX-118-TEX-I-1D462"></use></g><g data-mml-node="mo" transform="translate(572,0)"><use data-c="28" xlink:href="#MJX-118-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(961,0)"><use data-c="1D465" xlink:href="#MJX-118-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1533,0)"><use data-c="29" xlink:href="#MJX-118-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">u(x)</script><span> 为 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.865ex" height="2.23ex" role="img" focusable="false" viewBox="0 -974.6 1266.1 985.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-119-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-119-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-119-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msup"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-119-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(255.4,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-119-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-119-TEX-I-1D45B"></use></g><rect width="624.3" height="60" x="120" y="220"></rect></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow></msup></math></mjx-assistive-mml></mjx-container><script type="math/tex">x^{\frac{1}{n}}</script><span> 的负幂次级数, 在原点处, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.023ex" role="img" focusable="false" viewBox="0 -442 469 452" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.023ex;"><defs><path id="MJX-116-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-116-TEX-I-1D460"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">s</script><span> 为 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.865ex" height="2.23ex" role="img" focusable="false" viewBox="0 -974.6 1266.1 985.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-119-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-119-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 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data-mjx-texclass="ORD"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(255.4,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-119-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-119-TEX-I-1D45B"></use></g><rect width="624.3" height="60" x="120" y="220"></rect></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow></msup></math></mjx-assistive-mml></mjx-container><script type="math/tex">x^{\frac{1}{n}}</script><span> 的负次幂多项式, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.348ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1922 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: 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data-mml-node="mn" transform="translate(255.4,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-119-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-119-TEX-I-1D45B"></use></g><rect width="624.3" height="60" x="120" y="220"></rect></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow></msup></math></mjx-assistive-mml></mjx-container><script type="math/tex">x^{\frac{1}{n}}</script><span> 的正幂次级数. 这是本性奇点有代表性的表达形式. 当 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.506ex" height="1.692ex" role="img" focusable="false" viewBox="0 -666 2433.6 748" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.186ex;"><defs><path id="MJX-120-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-120-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-120-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≠</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n \neq 1</script><span> 时, 我们称这种解 为</span><mark><span>次常规解</span></mark><span> (subnormal solution), 次常规解的例子可见 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.891ex" height="1.532ex" role="img" focusable="false" viewBox="0 -677 1278 677" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-122-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path id="MJX-122-TEX-N-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path id="MJX-122-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><use data-c="34" xlink:href="#MJX-122-TEX-N-34"></use><use data-c="2E" xlink:href="#MJX-122-TEX-N-2E" transform="translate(500,0)"></use><use data-c="31" xlink:href="#MJX-122-TEX-N-31" transform="translate(778,0)"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">4.1</script><span> 节 [例 4.1.5].</span></p><blockquote><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" 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data-mml-node="mo"><use data-c="29" xlink:href="#MJX-168-TEX-N-29"></use></g><g data-mml-node="mn" transform="translate(422,363) scale(0.707)"><use data-c="33" xlink:href="#MJX-168-TEX-N-33"></use></g></g><g data-mml-node="mo" transform="translate(10496.3,0)"><use data-c="2B" xlink:href="#MJX-168-TEX-N-2B"></use></g><g data-mml-node="mo" transform="translate(11274.3,0)"><use data-c="22EF" xlink:href="#MJX-168-TEX-N-22EF"></use></g><g data-mml-node="mo" transform="translate(12446.3,0)"><use data-c="5D" xlink:href="#MJX-168-TEX-N-5D"></use></g></g></g></g></g><g data-mml-node="mtr" transform="translate(0,2376)"><g data-mml-node="mtd"><g data-mml-node="mtext"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">在</text></g><g data-mml-node="mtext" transform="translate(832,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">实</text></g><g data-mml-node="mtext" transform="translate(1664,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">轴</text></g><g data-mml-node="mtext" transform="translate(2496,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">上</text></g><g data-mml-node="mi" transform="translate(3328,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="832px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mi" transform="translate(4160,0)"><use data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(5009.8,0)"><use data-c="2192" xlink:href="#MJX-168-TEX-N-2192"></use></g><g data-mml-node="mo" transform="translate(6287.6,0)"><use data-c="2B" xlink:href="#MJX-168-TEX-N-2B"></use></g><g data-mml-node="mi" transform="translate(7065.6,0)"><use data-c="221E" xlink:href="#MJX-168-TEX-N-221E"></use></g><g data-mml-node="mo" transform="translate(8065.6,0)"><use data-c="2C" 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font-size="832px" font-family="serif">以</text></g><g data-mml-node="mi" transform="translate(10127.7,0)"><use data-c="221E" xlink:href="#MJX-168-TEX-N-221E"></use></g><g data-mml-node="mtext" transform="translate(11127.7,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">是</text></g><g data-mml-node="mtext" transform="translate(11959.7,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">本</text></g><g data-mml-node="mtext" transform="translate(12791.7,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">性</text></g><g data-mml-node="mtext" transform="translate(13623.7,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">奇</text></g><g data-mml-node="mtext" transform="translate(14455.7,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">点</text></g><g data-mml-node="TeXAtom" 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data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><g data-mml-node="mfrac" transform="translate(605,363) scale(0.707)"><g data-mml-node="mn" transform="translate(255.4,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-168-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-168-TEX-I-1D45B"></use></g><rect width="624.3" height="60" x="120" y="220"></rect></g></g><g data-mml-node="msup" transform="translate(4910.7,0)"><g data-mml-node="mo"><use data-c="29" xlink:href="#MJX-168-TEX-N-29"></use></g><g data-mml-node="TeXAtom" transform="translate(422,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2212" xlink:href="#MJX-168-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(778,0)"><use data-c="31" xlink:href="#MJX-168-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(6508.6,0)"><use data-c="2B" xlink:href="#MJX-168-TEX-N-2B"></use></g><g 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scale(0.707)"><use data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><rect width="604.5" height="60" x="120" y="220"></rect></g><g data-mml-node="msup" transform="translate(19040.1,0)"><g data-mml-node="mo"><use data-c="29" xlink:href="#MJX-168-TEX-N-29"></use></g><g data-mml-node="TeXAtom" transform="translate(422,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(255.4,394) scale(0.707)"><use data-c="32" xlink:href="#MJX-168-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-168-TEX-I-1D45B"></use></g><rect width="624.3" height="60" x="120" y="220"></rect></g></g></g><g data-mml-node="mo" transform="translate(20345.5,0)"><use data-c="2B" xlink:href="#MJX-168-TEX-N-2B"></use></g><g data-mml-node="mo" transform="translate(21345.7,0)"><use data-c="28" xlink:href="#MJX-168-TEX-N-28"></use></g><g data-mml-node="mfrac" transform="translate(21734.7,0)"><g data-mml-node="mn" transform="translate(245.5,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-168-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><rect width="604.5" height="60" x="120" y="220"></rect></g><g data-mml-node="msup" transform="translate(22579.2,0)"><g data-mml-node="mo"><use data-c="29" xlink:href="#MJX-168-TEX-N-29"></use></g><g data-mml-node="TeXAtom" transform="translate(422,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(255.4,394) scale(0.707)"><use data-c="33" xlink:href="#MJX-168-TEX-N-33"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-168-TEX-I-1D45B"></use></g><rect width="624.3" height="60" x="120" y="220"></rect></g></g></g><g data-mml-node="mo" transform="translate(23884.5,0)"><use data-c="2B" xlink:href="#MJX-168-TEX-N-2B"></use></g><g data-mml-node="mo" transform="translate(24884.7,0)"><use data-c="22EF" xlink:href="#MJX-168-TEX-N-22EF"></use></g><g data-mml-node="mtext" transform="translate(26223.4,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">在</text></g><g data-mml-node="mi" transform="translate(27055.4,0)"><use data-c="221E" xlink:href="#MJX-168-TEX-N-221E"></use></g><g data-mml-node="mtext" transform="translate(28055.4,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">处</text></g><g data-mml-node="mtext" transform="translate(28887.4,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">解</text></g><g data-mml-node="mtext" transform="translate(29719.4,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">析</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-2694.4)"><g 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transform="translate(7104.7,0)"><g data-mml-node="mn" transform="translate(245.5,394) scale(0.707)"><use data-c="31" xlink:href="#MJX-168-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(220,-345) scale(0.707)"><use data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><rect width="604.5" height="60" x="120" y="220"></rect></g><g data-mml-node="msup" transform="translate(7949.2,0)"><g data-mml-node="mo"><use data-c="29" xlink:href="#MJX-168-TEX-N-29"></use></g><g data-mml-node="TeXAtom" transform="translate(422,363) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(270,394)"><use data-c="33" xlink:href="#MJX-168-TEX-N-33"></use></g><g data-mml-node="mi" transform="translate(220,-345)"><use data-c="1D45B" xlink:href="#MJX-168-TEX-I-1D45B"></use></g><rect width="800" height="60" x="120" y="220"></rect></g></g></g><g data-mml-node="mo" transform="translate(9156.6,0)"><use data-c="2B" xlink:href="#MJX-168-TEX-N-2B"></use></g><g data-mml-node="mo" transform="translate(9934.6,0)"><use data-c="22EF" xlink:href="#MJX-168-TEX-N-22EF"></use></g><g data-mml-node="mo" transform="translate(11106.6,0)"><use data-c="5D" xlink:href="#MJX-168-TEX-N-5D"></use></g></g></g><g data-mml-node="mi" transform="translate(22598.5,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="832px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mn" transform="translate(23430.5,0)"><use data-c="30" xlink:href="#MJX-168-TEX-N-30"></use></g><g data-mml-node="mtext" transform="translate(23930.5,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">为</text></g><g data-mml-node="mtext" transform="translate(24762.5,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">本</text></g><g data-mml-node="mtext" transform="translate(25594.5,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">性</text></g><g data-mml-node="mtext" transform="translate(26426.5,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">奇</text></g><g data-mml-node="mtext" transform="translate(27258.5,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">异</text></g><g data-mml-node="mtext" transform="translate(28090.5,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">点</text></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(28922.5,0)"><g data-mml-node="mo"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">。</text></g></g></g></g><g data-mml-node="mtr" transform="translate(0,-4319)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="221E" xlink:href="#MJX-168-TEX-N-221E"></use></g><g data-mml-node="mtext" transform="translate(1000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">处</text></g><g data-mml-node="mi" transform="translate(1832,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="832px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mi" transform="translate(2664,0)"><use data-c="1D462" xlink:href="#MJX-168-TEX-I-1D462"></use></g><g data-mml-node="mo" transform="translate(3236,0)"><use data-c="28" xlink:href="#MJX-168-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(3625,0)"><use data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(4197,0)"><use data-c="29" xlink:href="#MJX-168-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(4863.8,0)"><use data-c="3D" xlink:href="#MJX-168-TEX-N-3D"></use></g><g data-mml-node="msup" transform="translate(5919.6,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-168-TEX-I-1D465"></use></g><g data-mml-node="mfrac" 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font-family="serif">处</text></g><g data-mml-node="mtext" transform="translate(15226.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">解</text></g><g data-mml-node="mtext" transform="translate(16058.6,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">析</text></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(16890.6,0)"><g data-mml-node="mo"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">。</text></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="left" columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi mathvariant="normal">∞</mi><mtext>处</mtext><mi>，</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">[</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><mo>⋯</mo><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">[</mo><mo stretchy="false">(</mo><msup><mi mathvariant="normal">∞</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msup><mi mathvariant="normal">∞</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi mathvariant="normal">∞</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mn>3</mn></msup><mo>+</mo><mo>⋯</mo><mo stretchy="false">]</mo></mrow></msup></mtd></mtr><mtr><mtd><mtext>在</mtext><mtext>实</mtext><mtext>轴</mtext><mtext>上</mtext><mi>，</mi><mi>x</mi><mo stretchy="false">→</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo>,</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mo>+</mo><mi mathvariant="normal">∞</mi></mtd></mtr><mtr><mtd><mi>x</mi><mo stretchy="false">→</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>,</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mn>0</mn><mo>,</mo><mtext>所</mtext><mtext>以</mtext><mi mathvariant="normal">∞</mi><mtext>是</mtext><mtext>本</mtext><mtext>性</mtext><mtext>奇</mtext><mtext>点</mtext><mrow data-mjx-texclass="ORD"><mo>。</mo></mrow></mtd></mtr><mtr><mtd><mi>u</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>=</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>2</mn><mi>n</mi></mfrac></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>3</mn><mi>n</mi></mfrac></mrow></msup><mo>+</mo><mo>⋯</mo><mtext>在</mtext><mi mathvariant="normal">∞</mi><mtext>处</mtext><mtext>解</mtext><mtext>析</mtext></mtd></mtr><mtr><mtd><mn>0</mn><mtext>处</mtext><mi>，</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">[</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo stretchy="false">]</mo></mrow></msup><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>2</mn><mi>n</mi></mfrac></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>3</mn><mi>n</mi></mfrac></mrow></msup><mo>+</mo><mo>⋯</mo><mo stretchy="false">]</mo></mrow></msup><mi>，</mi><mn>0</mn><mtext>为</mtext><mtext>本</mtext><mtext>性</mtext><mtext>奇</mtext><mtext>异</mtext><mtext>点</mtext><mrow data-mjx-texclass="ORD"><mo>。</mo></mrow></mtd></mtr><mtr><mtd><mi mathvariant="normal">∞</mi><mtext>处</mtext><mi>，</mi><mi>u</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><mo>⋯</mo><mo>,</mo><mn>0</mn><mtext>处</mtext><mtext>解</mtext><mtext>析</mtext><mrow data-mjx-texclass="ORD"><mo>。</mo></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div></blockquote><blockquote><p><span>airy函数是次常规的</span></p></blockquote><h3 id='-例-431-求解-hermite-方程'><span>[ 例 4.3.1] 求解 Hermite 方程</span></h3><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n260" cid="n260" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="21.802ex" height="2.791ex" role="img" focusable="false" viewBox="0 -883.9 9636.5 1233.4" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: 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xlink:href="#MJX-169-TEX-N-2B"></use></g><g data-mml-node="mrow" transform="translate(2345.4,0)"><g data-mml-node="mo" transform="translate(0 -0.5)"><use data-c="28" xlink:href="#MJX-169-TEX-SO-28"></use></g><g data-mml-node="mi" transform="translate(458,0)"><use data-c="1D706" xlink:href="#MJX-169-TEX-I-1D706"></use></g><g data-mml-node="mo" transform="translate(1263.2,0)"><use data-c="2212" xlink:href="#MJX-169-TEX-N-2212"></use></g><g data-mml-node="msup" transform="translate(2263.4,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-169-TEX-I-1D6FC"></use></g><g data-mml-node="TeXAtom" transform="translate(673,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-169-TEX-N-32"></use></g></g></g><g data-mml-node="msup" transform="translate(3340,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-169-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-169-TEX-N-32"></use></g></g></g><g data-mml-node="mo" transform="translate(4348.6,0) translate(0 -0.5)"><use data-c="29" xlink:href="#MJX-169-TEX-SO-29"></use></g></g><g data-mml-node="mi" transform="translate(7151.9,0)"><use data-c="1D713" xlink:href="#MJX-169-TEX-I-1D713"></use></g><g data-mml-node="mo" transform="translate(8080.7,0)"><use data-c="3D" xlink:href="#MJX-169-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(9136.5,0)"><use data-c="30" xlink:href="#MJX-169-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>ψ</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>λ</mi><mo>−</mo><msup><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>ψ</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><blockquote><p><span>没有第二个梯子（</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.929ex" height="2.283ex" role="img" focusable="false" viewBox="0 -759 2620.5 1009" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-123-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 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xlink:href="#MJX-123-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1464,0)"><use data-c="29" xlink:href="#MJX-123-TEX-N-29"></use></g><g data-mml-node="msup" transform="translate(1853,0)"><g data-mml-node="mi"><use data-c="1D466" xlink:href="#MJX-123-TEX-I-1D466"></use></g><g data-mml-node="mo" transform="translate(523,363) scale(0.707)"><use data-c="2032" xlink:href="#MJX-123-TEX-V-2032"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><msup><mi>y</mi><mo data-mjx-alternate="1">′</mo></msup></math></mjx-assistive-mml></mjx-container><script type="math/tex">p(x)y'</script><span>），一定不满足定理一二。</span></p></blockquote><p><span>在 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.262ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 1000 453" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-126-TEX-N-221E" d="M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="221E" xlink:href="#MJX-126-TEX-N-221E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∞</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\infty</script><span> 处的渐近解, 其中 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="3.773ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 1667.7 888" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-125-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path><path id="MJX-125-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 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transform="translate(1027.7,0)"><use data-c="1D6FC" xlink:href="#MJX-125-TEX-I-1D6FC"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>,</mo><mi>α</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\lambda, \alpha</script><span> 为常数.</span>
<span>因为 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.262ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 1000 453" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-126-TEX-N-221E" d="M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="221E" xlink:href="#MJX-126-TEX-N-221E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∞</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\infty</script><span> 为非正则奇点, 且不满足定理一的条件, 所以我们必须 假定</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n264" cid="n264" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="16.363ex" height="2.7ex" role="img" focusable="false" viewBox="0 -943.3 7232.5 1193.3" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path 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data-mml-node="math"><g data-mml-node="mi"><use data-c="1D713" xlink:href="#MJX-170-TEX-I-1D713"></use></g><g data-mml-node="mo" transform="translate(651,0)"><use data-c="28" xlink:href="#MJX-170-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1040,0)"><use data-c="1D465" xlink:href="#MJX-170-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1612,0)"><use data-c="29" xlink:href="#MJX-170-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2278.8,0)"><use data-c="3D" xlink:href="#MJX-170-TEX-N-3D"></use></g><g data-mml-node="msup" transform="translate(3334.6,0)"><g data-mml-node="mi"><use data-c="1D452" xlink:href="#MJX-170-TEX-I-1D452"></use></g><g data-mml-node="TeXAtom" transform="translate(499,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D444" xlink:href="#MJX-170-TEX-I-1D444"></use></g><g data-mml-node="mo" transform="translate(791,0)"><use data-c="28" xlink:href="#MJX-170-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1180,0)"><use data-c="1D465" xlink:href="#MJX-170-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1752,0)"><use data-c="29" xlink:href="#MJX-170-TEX-N-29"></use></g></g></g><g data-mml-node="mi" transform="translate(5397.5,0)"><use data-c="1D463" xlink:href="#MJX-170-TEX-I-1D463"></use></g><g data-mml-node="mo" transform="translate(5882.5,0)"><use data-c="28" xlink:href="#MJX-170-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(6271.5,0)"><use data-c="1D465" xlink:href="#MJX-170-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(6843.5,0)"><use data-c="29" xlink:href="#MJX-170-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>ψ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></msup><mi>v</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container></div></div><p><span>在上述变换下, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.097ex" height="1.027ex" role="img" focusable="false" viewBox="0 -443 485 454" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-127-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D463" xlink:href="#MJX-127-TEX-I-1D463"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">v</script><span> 的方程为</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n266" cid="n266" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="22.954ex" height="2.396ex" role="img" focusable="false" viewBox="0 -809 10145.8 1059" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-171-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-171-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-171-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 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scale(0.707)"><use data-c="33" xlink:href="#MJX-128-TEX-N-33"></use></g></g><g data-mml-node="mo" transform="translate(12369.2,0)"><use data-c="2B" xlink:href="#MJX-128-TEX-N-2B"></use></g><g data-mml-node="mo" transform="translate(13369.4,0)"><use data-c="22EF" xlink:href="#MJX-128-TEX-N-22EF"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>+</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mi>n</mi></mfrac></msup><msup><mo stretchy="false">)</mo><mn>3</mn></msup><mo>+</mo><mo>⋯</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">Q(x)=x^\frac 1 n+(x^\frac 1 n)^2+(x^\frac 1 n)^3+\cdots </script></p><p><span>设Q(x)的最高次幂是n</span></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.192ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1853 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-129-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path><path id="MJX-129-TEX-N-7E" d="M179 251Q164 251 151 245T131 234T111 215L97 227L83 238Q83 239 95 253T121 283T142 304Q165 318 187 318T253 300T320 282Q335 282 348 288T368 299T388 318L402 306L416 295Q375 236 344 222Q330 215 313 215Q292 215 248 233T179 251Z"></path><path id="MJX-129-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-129-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-129-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mover"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-129-TEX-I-1D45D"></use></g><g data-mml-node="mo" transform="translate(334.8,332) translate(-250 0)"><use data-c="7E" xlink:href="#MJX-129-TEX-N-7E"></use></g></g></g><g data-mml-node="mo" transform="translate(503,0)"><use data-c="28" xlink:href="#MJX-129-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(892,0)"><use data-c="1D465" xlink:href="#MJX-129-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1464,0)"><use data-c="29" xlink:href="#MJX-129-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">~</mo></mover></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">\tilde{p}(x)</script><span>最高次幂：n-1</span></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.095ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1810 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d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mover"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-130-TEX-I-1D45E"></use></g><g data-mml-node="mo" transform="translate(316.8,332) translate(-250 0)"><use data-c="7E" xlink:href="#MJX-130-TEX-N-7E"></use></g></g></g><g data-mml-node="mo" transform="translate(460,0)"><use data-c="28" xlink:href="#MJX-130-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(849,0)"><use data-c="1D465" xlink:href="#MJX-130-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1421,0)"><use data-c="29" xlink:href="#MJX-130-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo stretchy="false">~</mo></mover></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">\tilde{q}(x)</script><span>最高次幂：max[0,2，n-2,2n-2]</span></p><p><span>回顾定理一：</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n275" cid="n275" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="40.301ex" height="9.513ex" role="img" focusable="false" viewBox="0 -2352.3 17812.9 4204.6" 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xlink:href="#MJX-173-TEX-I-1D452"></use></g><g data-mml-node="mi" transform="translate(9557.8,0)"><use data-c="1D45B" xlink:href="#MJX-173-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(10157.8,0)"><use data-c="1D456" xlink:href="#MJX-173-TEX-I-1D456"></use></g><g data-mml-node="mi" transform="translate(10502.8,0)"><use data-c="1D462" xlink:href="#MJX-173-TEX-I-1D462"></use></g><g data-mml-node="mi" transform="translate(11074.8,0)"><use data-c="1D460" xlink:href="#MJX-173-TEX-I-1D460"></use></g><g data-mml-node="mtext" transform="translate(11543.8,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">级</text></g><g data-mml-node="mtext" transform="translate(12375.8,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">数</text></g><g data-mml-node="mtext" transform="translate(13207.8,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">解</text></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="left" columnspacing="1em" rowspacing="4pt"><mtr><mtd><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>x</mi></mfrac><mo>+</mo><mo>⋯</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd><mtd><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mi>x</mi></mfrac><mo>+</mo><mo>⋯</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd><mtd><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></mtd></mtr><mtr><mtd><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>≥</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>+</mo><mn>1</mn><mo>,</mo><mtext>有</mtext><mi>F</mi><mi>r</mi><mi>o</mi><mi>u</mi><mi>b</mi><mi>e</mi><mi>n</mi><mi>i</mi><mi>u</mi><mi>s</mi><mtext>级</mtext><mtext>数</mtext><mtext>解</mtext></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>所以，需要</span><mjx-container 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transform="translate(4534,0)"><use data-c="1D44E" xlink:href="#MJX-131-TEX-I-1D44E"></use></g><g data-mml-node="mi" transform="translate(5063,0)"><use data-c="1D465" xlink:href="#MJX-131-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(5635,0)"><use data-c="5B" xlink:href="#MJX-131-TEX-N-5B"></use></g><g data-mml-node="mn" transform="translate(5913,0)"><use data-c="30" xlink:href="#MJX-131-TEX-N-30"></use></g><g data-mml-node="mo" transform="translate(6413,0)"><use data-c="2C" xlink:href="#MJX-131-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(6857.7,0)"><use data-c="32" xlink:href="#MJX-131-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(7357.7,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="884px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mi" transform="translate(8189.7,0)"><use data-c="1D45B" xlink:href="#MJX-131-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(9011.9,0)"><use data-c="2212" xlink:href="#MJX-131-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(10012.1,0)"><use data-c="32" xlink:href="#MJX-131-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(10512.1,0)"><use data-c="2C" xlink:href="#MJX-131-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(10956.8,0)"><use data-c="32" xlink:href="#MJX-131-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(11456.8,0)"><use data-c="1D45B" xlink:href="#MJX-131-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(12279,0)"><use data-c="2212" xlink:href="#MJX-131-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(13279.2,0)"><use data-c="32" xlink:href="#MJX-131-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(13779.2,0)"><use data-c="5D" xlink:href="#MJX-131-TEX-N-5D"></use></g><g data-mml-node="mo" transform="translate(14279.4,0)"><use data-c="2B" xlink:href="#MJX-131-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(15279.7,0)"><use data-c="31" xlink:href="#MJX-131-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>−</mo><mn>1</mn><mo>≥</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>，</mi><mi>n</mi><mo>−</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn><mo stretchy="false">]</mo><mo>+</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n-1\ge max[0,2，n-2,2n-2]+1</script><span>,即</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="33.563ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 14835 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-132-TEX-I-1D45B" d="M21 287Q22 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data-mml-node="mn" transform="translate(5378.4,0)"><use data-c="31" xlink:href="#MJX-174-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(5878.4,0)"><use data-c="2C" xlink:href="#MJX-174-TEX-N-2C"></use></g></g><g data-mml-node="mtd" transform="translate(10032.9,0)"><g data-mml-node="mo"><use data-c="2192" xlink:href="#MJX-174-TEX-N-2192"></use></g><g data-mml-node="mi" transform="translate(1277.8,0)"><use data-c="1D45B" xlink:href="#MJX-174-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(2155.6,0)"><use data-c="2265" xlink:href="#MJX-174-TEX-N-2265"></use></g><g data-mml-node="mn" transform="translate(3211.3,0)"><use data-c="34" xlink:href="#MJX-174-TEX-N-34"></use></g><g data-mml-node="mn" transform="translate(3711.3,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">①</text></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-174-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(822.2,0)"><use data-c="2212" xlink:href="#MJX-174-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(1822.4,0)"><use data-c="31" xlink:href="#MJX-174-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(2600.2,0)"><use data-c="2265" xlink:href="#MJX-174-TEX-N-2265"></use></g><g data-mml-node="mi" transform="translate(3656,0)"><use data-c="1D45B" xlink:href="#MJX-174-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(4478.2,0)"><use data-c="2212" xlink:href="#MJX-174-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(5478.4,0)"><use data-c="32" xlink:href="#MJX-174-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(6200.7,0)"><use data-c="2B" xlink:href="#MJX-174-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(7200.9,0)"><use data-c="31" xlink:href="#MJX-174-TEX-N-31"></use></g><g data-mml-node="mo" transform="translate(7700.9,0)"><use data-c="2C" xlink:href="#MJX-174-TEX-N-2C"></use></g></g><g data-mml-node="mtd" transform="translate(10032.9,0)"><g data-mml-node="mo"><use data-c="2192" xlink:href="#MJX-174-TEX-N-2192"></use></g><g data-mml-node="mi" transform="translate(1277.8,0)"><use data-c="1D45B" xlink:href="#MJX-174-TEX-I-1D45B"></use></g><g data-mml-node="mtext" transform="translate(1877.8,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">任</text></g><g data-mml-node="mtext" transform="translate(2709.8,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">意</text></g><g data-mml-node="mn" transform="translate(3541.8,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">②</text></g></g></g><g data-mml-node="mtr" transform="translate(0,-1200)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-174-TEX-I-1D45B"></use></g><g 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xlink:href="#MJX-174-TEX-N-31"></use></g><g data-mml-node="mi" transform="translate(8200.9,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="832px" font-family="serif" font-style="italic">，</text></g></g><g data-mml-node="mtd" transform="translate(10032.9,0)"><g data-mml-node="mo"><use data-c="2192" xlink:href="#MJX-174-TEX-N-2192"></use></g><g data-mml-node="mi" transform="translate(1277.8,0)"><use data-c="1D45B" xlink:href="#MJX-174-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(2155.6,0)"><use data-c="2264" xlink:href="#MJX-174-TEX-N-2264"></use></g><g data-mml-node="mn" transform="translate(3211.3,0)"><use data-c="30" xlink:href="#MJX-174-TEX-N-30"></use></g><g data-mml-node="mn" transform="translate(3711.3,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="832px" font-family="serif">③</text></g></g></g></g><g data-mml-node="mo" transform="translate(15465.2,0) translate(0 250)"></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mtable columnalign="left left" columnspacing="1em" rowspacing=".2em"><mtr><mtd><mi>n</mi><mo>−</mo><mn>1</mn><mo>≥</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>,</mo></mtd><mtd><mo accent="false" stretchy="false">→</mo><mi>n</mi><mo>≥</mo><mn>4</mn><mn>①</mn></mtd></mtr><mtr><mtd><mi>n</mi><mo>−</mo><mn>1</mn><mo>≥</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>,</mo></mtd><mtd><mo accent="false" stretchy="false">→</mo><mi>n</mi><mtext>任</mtext><mtext>意</mtext><mn>②</mn></mtd></mtr><mtr><mtd><mi>n</mi><mo>−</mo><mn>1</mn><mo>≥</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn><mo>+</mo><mn>1</mn><mi>，</mi></mtd><mtd><mo accent="false" stretchy="false">→</mo><mi>n</mi><mo>≤</mo><mn>0</mn><mn>③</mn></mtd></mtr></mtable><mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo></mrow></math></mjx-assistive-mml></mjx-container></div></div><p><span>无解，因为没有考虑2,n-2,2n-2中有抵消的情况。</span>
<span>考虑抵消。如果n-2,2n-2项相互抵消，n-2=2n-2,n=0。且由①</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.506ex" height="1.844ex" role="img" focusable="false" viewBox="0 -677 2433.6 815" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.312ex;"><defs><path id="MJX-133-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-133-TEX-N-2265" d="M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-133-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-133-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(877.8,0)"><use data-c="2265" xlink:href="#MJX-133-TEX-N-2265"></use></g><g data-mml-node="mn" transform="translate(1933.6,0)"><use data-c="34" xlink:href="#MJX-133-TEX-N-34"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≥</mo><mn>4</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n\ge4</script><span>,相矛盾。</span></p><p><span>                   如果2，n-2项相抵消，2=n-2，n=4.且由③</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.506ex" height="1.819ex" role="img" focusable="false" viewBox="0 -666 2433.6 804" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.312ex;"><defs><path id="MJX-134-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-134-TEX-N-2264" d="M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z"></path><path id="MJX-134-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJX-134-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(877.8,0)"><use data-c="2264" xlink:href="#MJX-134-TEX-N-2264"></use></g><g data-mml-node="mn" transform="translate(1933.6,0)"><use data-c="30" xlink:href="#MJX-134-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≤</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">n\le 0</script><span>,相矛盾。</span></p><p><span>                   如果2,2n-2项相抵消，n=2.与②不矛盾</span></p><p><span>n=2,所以，</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n283" cid="n283" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container 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xlink:href="#MJX-176-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(2124.6,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJX-176-TEX-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-686)"><use data-c="32" xlink:href="#MJX-176-TEX-N-32"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mi" transform="translate(3064.6,0)"><use data-c="1D6FC" xlink:href="#MJX-176-TEX-I-1D6FC"></use></g><g data-mml-node="msup" transform="translate(3704.6,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-176-TEX-I-1D465"></use></g><g data-mml-node="mn" transform="translate(605,413) scale(0.707)"><use data-c="32" xlink:href="#MJX-176-TEX-N-32"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">~</mo></mover></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo stretchy="false">~</mo></mover></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>q</mi><mo>+</mo><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>+</mo><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>λ</mi><mo>−</mo><msup><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>+</mo><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn><mtext>项</mtext><mtext>相</mtext><mtext>抵</mtext><mtext>消</mtext><mo>,</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><msup><mi>α</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>,</mo><mo>±</mo><mi>α</mi><mi>x</mi><mo>=</mo><msup><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mi>Q</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>α</mi><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p>&nbsp;</p></blockquote><p><span>按照定理一的结论, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.138ex" height="2.136ex" role="img" focusable="false" viewBox="0 -750 503 944" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-135-TEX-I-1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 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xlink:href="#MJX-136-TEX-N-7E"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo stretchy="false">~</mo></mover></mrow></math></mjx-assistive-mml></mjx-container><script type="math/tex">\tilde{q}</script><span> 的阶数, 必须要求 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.79ex" height="2.032ex" role="img" focusable="false" viewBox="0 -704 791 898" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-137-TEX-I-1D444" d="M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 -60T625 -3Q631 11 638 11Q647 11 649 2Q649 -6 639 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transform="translate(3474.6,0)"><use data-c="B1" xlink:href="#MJX-177-TEX-N-B1"></use></g><g data-mml-node="mfrac" transform="translate(4252.6,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D6FC" xlink:href="#MJX-177-TEX-I-1D6FC"></use></g><g data-mml-node="mn" transform="translate(290,-686)"><use data-c="32" xlink:href="#MJX-177-TEX-N-32"></use></g><rect width="840" height="60" x="120" y="220"></rect></g><g data-mml-node="msup" transform="translate(5332.6,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-177-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-177-TEX-N-32"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>Q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo>±</mo><mfrac><mi>α</mi><mn>2</mn></mfrac><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></math></mjx-assistive-mml></mjx-container></div></div><p><span>所以, </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.152ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1835 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-139-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 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278H58Q52 284 52 289Z"></path><path id="MJX-139-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D463" xlink:href="#MJX-139-TEX-I-1D463"></use></g><g data-mml-node="mo" transform="translate(485,0)"><use data-c="28" xlink:href="#MJX-139-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(874,0)"><use data-c="1D465" xlink:href="#MJX-139-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1446,0)"><use data-c="29" xlink:href="#MJX-139-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">v(x)</script><span> 所满足的方程 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="7.543ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3334 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-140-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-140-TEX-N-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 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93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-140-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-140-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g 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stretchy="false">(</mo><mn>4.3</mn><mn>.20</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">(4.3 .20)</script><span> 为</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n289" cid="n289" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="25.833ex" height="2.396ex" role="img" focusable="false" viewBox="0 -809 11418.3 1059" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-178-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-178-TEX-V-2032" d="M79 43Q73 43 52 49T30 61Q30 68 85 293T146 528Q161 560 198 560Q218 560 240 545T262 501Q262 496 260 486Q259 479 173 263T84 45T79 43Z"></path><path id="MJX-178-TEX-N-B1" d="M56 320T56 333T70 353H369V502Q369 651 371 655Q376 666 388 666Q402 666 405 654T409 596V500V353H707Q722 345 722 333Q722 320 707 313H409V40H707Q722 32 722 20T707 0H70Q56 7 56 20T70 40H369V313H70Q56 320 56 333Z"></path><path id="MJX-178-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-178-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-178-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 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data-mml-node="mi" transform="translate(2679.4,0)"><use data-c="1D6FC" xlink:href="#MJX-178-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(3319.4,0)"><use data-c="1D465" xlink:href="#MJX-178-TEX-I-1D465"></use></g><g data-mml-node="msup" transform="translate(3891.4,0)"><g data-mml-node="mi"><use data-c="1D463" xlink:href="#MJX-178-TEX-I-1D463"></use></g><g data-mml-node="TeXAtom" transform="translate(518,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="2032" xlink:href="#MJX-178-TEX-V-2032"></use></g></g></g><g data-mml-node="mo" transform="translate(4876,0)"><use data-c="2B" xlink:href="#MJX-178-TEX-N-2B"></use></g><g data-mml-node="mo" transform="translate(5876.3,0)"><use data-c="28" xlink:href="#MJX-178-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(6265.3,0)"><use data-c="1D706" xlink:href="#MJX-178-TEX-I-1D706"></use></g><g data-mml-node="mo" transform="translate(7070.5,0)"><use data-c="B1" xlink:href="#MJX-178-TEX-N-B1"></use></g><g data-mml-node="mi" transform="translate(8070.7,0)"><use data-c="1D6FC" xlink:href="#MJX-178-TEX-I-1D6FC"></use></g><g data-mml-node="mo" transform="translate(8710.7,0)"><use data-c="29" xlink:href="#MJX-178-TEX-N-29"></use></g><g data-mml-node="mi" transform="translate(9099.7,0)"><use data-c="1D463" xlink:href="#MJX-178-TEX-I-1D463"></use></g><g data-mml-node="mo" transform="translate(9862.5,0)"><use data-c="3D" xlink:href="#MJX-178-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(10918.3,0)"><use data-c="30" xlink:href="#MJX-178-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>±</mo><mn>2</mn><mi>α</mi><mi>x</mi><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mi>λ</mi><mo>±</mo><mi>α</mi><mo stretchy="false">)</mo><mi>v</mi><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container></div></div><p><span>该方程符合定理一的条件, 可令</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n291" cid="n291" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="16.474ex" height="6.399ex" role="img" focusable="false" viewBox="0 -1562.5 7281.4 2828.3" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -2.864ex;"><defs><path id="MJX-179-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 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-11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-179-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-179-TEX-LO-2211" d="M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 898T699 902H574H543H251L259 891Q722 258 724 252Q725 250 724 246Q721 243 460 -56L196 -356Q196 -357 407 -357Q459 -357 548 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data-mml-node="mi"><use data-c="221E" xlink:href="#MJX-179-TEX-N-221E"></use></g></g></g><g data-mml-node="msub" transform="translate(4616.5,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-179-TEX-I-1D6FC"></use></g><g data-mml-node="TeXAtom" transform="translate(673,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-179-TEX-I-1D458"></use></g></g></g><g data-mml-node="msup" transform="translate(5707.9,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-179-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2212" xlink:href="#MJX-179-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(778,0)"><use data-c="1D458" xlink:href="#MJX-179-TEX-I-1D458"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>v</mi><mo>=</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>ρ</mi></mrow></msup><munderover><mo data-mjx-texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mo>−</mo><mi>k</mi></mrow></msup></math></mjx-assistive-mml></mjx-container></div></div><p><span>得特征指数为</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n293" cid="n293" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="10.715ex" height="4.676ex" role="img" focusable="false" viewBox="0 -1370 4736 2067" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.577ex;"><defs><path id="MJX-180-TEX-I-1D70C" d="M58 -216Q25 -216 23 -186Q23 -176 73 26T127 234Q143 289 182 341Q252 427 341 441Q343 441 349 441T359 442Q432 442 471 394T510 276Q510 219 486 165T425 74T345 13T266 -10H255H248Q197 -10 165 35L160 41L133 -71Q108 -168 104 -181T92 -202Q76 -216 58 -216ZM424 322Q424 359 407 382T357 405Q322 405 287 376T231 300Q217 269 193 170L176 102Q193 26 260 26Q298 26 334 62Q367 92 389 158T418 266T424 322Z"></path><path id="MJX-180-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-180-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path><path id="MJX-180-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-180-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-180-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 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transform="translate(1805.4,0)"><use data-c="1D6FC" xlink:href="#MJX-180-TEX-I-1D6FC"></use></g></g><g data-mml-node="mrow" transform="translate(872.7,-686)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-180-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(500,0)"><use data-c="1D6FC" xlink:href="#MJX-180-TEX-I-1D6FC"></use></g></g><rect width="2645.4" height="60" x="120" y="220"></rect></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>ρ</mi><mo>=</mo><mfrac><mrow><mi>λ</mi><mo>−</mo><mi>α</mi></mrow><mrow><mn>2</mn><mi>α</mi></mrow></mfrac></math></mjx-assistive-mml></mjx-container></div></div><p><span>系数的递推方程为</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n295" cid="n295" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div 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